e-books in Category Theory category
by Brendan Fong, David I Spivak - arXiv.org , 2018
This book is an invitation to discover advanced topics in category theory through concrete, real-world examples. The tour takes place over seven sketches, such as databases, electric circuits, etc, with the exploration of a categorical structure.
(916 views)
by Bartosz Milewski - unglue.it , 2017
Category theory is the kind of math that is particularly well suited for the minds of programmers. It deals with the kind of structure that makes programs composable. And I will argue strongly that composition is the essence of programming.
(1304 views)
by David I. Spivak - The MIT Press , 2014
This book shows that category theory can be useful outside of mathematics as a flexible modeling language throughout the sciences. Written in an engaging and straightforward style, the book is rigorous but accessible to non-mathematicians.
(1445 views)
by Tom Leinster - arXiv , 2016
This introduction to category theory is for readers with relatively little mathematical background. At its heart is the concept of a universal property, important throughout mathematics. For each new concept a generous supply of examples is provided.
(1905 views)
by D. I. Spivak, C. Vasilakopoulou, P. Schultz - arXiv , 2016
A categorical framework for modeling and analyzing systems in a broad sense is proposed. These systems should be thought of as 'machines' with inputs and outputs, carrying some sort of signal that occurs through some notion of time.
(1323 views)
by Peter Smith - Logic Matters , 2016
I hope that what is here may prove useful to others starting to get to grips with category theory. This text is intended to be relatively accessible; in particular, it presupposes rather less mathematical background than some texts on categories.
(2253 views)
by Takahiro Kato - viXra.org , 2015
Modules and morphisms among them subsume categories and functors and provide more general framework to explore the theory of structures. In this book we generalize the basic notions and results of category theory using this framework of modules.
(3272 views)
by Sen Hu, Xuexing Lu, Yu Ye - arXiv , 2015
In this paper, we reveal the combinatorial nature of tensor calculus for strict tensor categories and show that there exists a monad which is described by the coarse-graining of graphs and characterizes the algebraic nature of tensor calculus.
(2179 views)
by David I. Spivak - arXiv , 2013
We attempt to show that category theory can be applied throughout the sciences as a framework for modeling phenomena and communicating results. In order to target the scientific audience, this book is example-based rather than proof-based.
(5089 views)
by Pierre Schapira - UPMC , 2011
These notes introduce the language of categories and present the basic notions of homological algebra, first from an elementary point of view, next with a more sophisticated approach, with the introduction of triangulated and derived categories.
(5176 views)
by Michael Barr, Charles Wells - Prentice Hall , 1998
This book is a textbook in basic category theory, written specifically to be read by researchers and students in computing science. We expound the constructions basic to category theory in the context of applications to computing science.
(4385 views)
by J. Cigler, V. Losert, P.W. Michor - Marcel Dekker Inc , 1979
This book is the final outgrowth of a sequence of seminars about functors on categories of Banach spaces (held 1971 - 1975) and several doctoral dissertations. It has been written for readers with a general background in functional analysis.
(5332 views)
by Peter W. Michor - Springer , 1978
The aim of this book is to develop the theory of Banach operator ideals and metric tensor products along categorical lines: these two classes of mathematical objects are endofunctors on the category Ban of all Banach spaces in a natural way.
(5656 views)
by Mikael Vejdemo-Johansson - University of St. Andrews , 2012
An introduction to category theory that ties into Haskell and functional programming as a source of applications. Topics: definition of categories, special objects and morphisms, functors, natural transformation, (co-)limits and special cases, etc.
(7280 views)
by Jacob Lurie - Princeton University Press , 2009
Jacob Lurie presents the foundations of higher category theory, using the language of weak Kan complexes, and shows how existing theorems in algebraic topology can be reformulated and generalized in the theory's new language.
(6880 views)
by Jacob Lurie - Harvard University , 2017
Contents: Stable infinite-Categories; infinite-Operads; Algebras and Modules over infinte-Operads; Associative Algebras and Their Modules; Little Cubes and Factorizable Sheaves; Algebraic Structures on infinite-Categories; and more.
(10003 views)
by Samson Abramsky, Nikos Tzevelekos - arXiv , 2011
These notes provide a succinct, accessible introduction to some of the basic ideas of category theory and categorical logic. The main prerequisite is a basic familiarity with the elements of discrete mathematics: sets, relations and functions.
(7088 views)
by Daniele Turi - University of Edinburgh , 2001
These notes were written for a course in category theory. The course was designed to be self-contained, drawing most of the examples from category theory itself. It was intended for post-graduate students in theoretical computer science.
(6504 views)
by A. Schalk, H. Simmons - Manchester University , 2005
Notes for a course offered as part of the MSc. in Mathematical Logic. From the table of contents: Development and exercises; Functors and natural transformations; Limits and colimits, a universal solution; Cartesian closed categories.
(7165 views)
by Michael Barr, Charles Wells , 1999
Categories originally arose in mathematics out of the need of a formalism to describe the passage from one type of mathematical structure to another. These notes form a short summary of some major topics in category theory.
(7126 views)
- Wikibooks , 2010
This book is an introduction to category theory, written for those who have some understanding of one or more branches of abstract mathematics, such as group theory, analysis or topology. It contains examples drawn from various branches of math.
(7111 views)
by Jaap van Oosten - University of Utrecht , 2007
Contents: Categories and Functors; Natural transformations; (Co)cones and (Co)limits; A little piece of categorical logic; Adjunctions; Monads and Algebras; Cartesian closed categories and the lambda-calculus; Recursive Domain Equations.
(7207 views)
by Peter Freyd - Harper and Row , 1964
From the table of contents: Fundamentals (Contravariant functors and dual categories); Fundamentals of Abelian categories; Special functors and subcategories; Metatheorems; Functor categories; Injective envelopes; Embedding theorems.
(7464 views)
by Paul Goerss, Kristen Schemmerhorn - Northwestern University , 2004
There are many ways to present model categories, each with a different point of view. Here we would like to treat model categories as a way to build and control resolutions. We are going to emphasize the analog of projective resolutions.
(5439 views)
by P. J. Higgins - Van Nostrand Reinhold , 1971
A self-contained account of the elementary theory of groupoids and some of its uses in group theory and topology. Category theory appears as a secondary topic whenever it is relevant to the main issue, and its treatment is by no means systematic.
(9653 views)
by B. Eckmann - Springer , 1969
This volume concentrates a) on the concept of 'triple' or standard construction with special reference to the associated 'algebras', and b) on homology theories in general categories, based upon triples and simplicial methods.
(6863 views)
by Tom Leinster - arXiv , 2003
Higher-dimensional category theory is the study of n-categories, operads, braided monoidal categories, and other such exotic structures. It draws its inspiration from topology, quantum algebra, mathematical physics, logic, and computer science.
(7471 views)
by Eugenia Cheng, Aaron Lauda - University of Sheffield , 2004
This work gives an explanatory introduction to various definitions of higher-dimensional category. The emphasis is on ideas rather than formalities; the aim is to shed light on the formalities by emphasizing the intuitions that lead there.
(8119 views)
by Marc Levine - American Mathematical Society , 1998
This book combines foundational constructions in the theory of motives and results relating motivic cohomology to more explicit constructions. Prerequisite for understanding the work is a basic background in algebraic geometry.
(9630 views)
by Maarten M. Fokkinga - University of Twente , 1994
These notes present the important notions from category theory. The intention is to provide a fairly good skill in manipulating with those concepts formally. This text introduces category theory in the calculational style of the proofs.
(13206 views)
by D.E. Rydeheard, R.M. Burstall , 2001
The book is a bridge-building exercise between computer programming and category theory. Basic constructions of category theory are expressed as computer programs. It is a first attempt at connecting the abstract mathematics with concrete programs.
(12489 views)
by Andrea Asperti, Giuseppe Longo - MIT Press , 1991
Here is an introduction to category theory for the working computer scientist. It is a self-contained introduction to general category theory and the mathematical structures that constitute the theoretical background.
(12324 views)
by Jiri Adamek, Horst Herrlich, George Strecker - John Wiley & Sons , 1990
A modern introduction to the theory of structures via the language of category theory, the emphasis is on concrete categories. The first five chapters present the basic theory, while the last two contain more recent research results.
(12531 views)
by Max Kelly - Cambridge University Press , 2005
The book presents a selfcontained account of basic category theory, assuming as prior knowledge only the most elementary categorical concepts. It is designed to supply a connected account of the theory, or at least of a substantial part of it.
(8400 views)
by Michael Barr, Charles Wells - Springer-Verlag , 2005
Introduction to toposes, triples and theories and the connections between them. The book starts with an introduction to category theory, then introduces each of the three topics of the title. Exercises provide examples or develop the theory further.
(9406 views)